22. April 2026
Łukasz Michalak (Adam Mickiewicz University Poznań)
The symplectic representation of the mapping class group of a surface
The mapping class group of an orientable surface has a natural symplectic representation given by its action on the first homology group. In this talk we will discuss what can be read from this representation about the Nielsen--Thurston classification and what dynamical information it carries. In particular, we will present our version of the Casson--Bleiler criterion for cyclotomic polynomials, which gives a homological condition ensuring pseudo-Anosov behavior. We will also discuss which homological data can be realized by Morse--Smale diffeomorphisms, and how, in this case, homology reflects the structure of periodic points.